Integrate X^3sin(x^2) | No Substitutions, No Chaos

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Homework Help Overview

The discussion revolves around the integration of the function X^3sin(x^2), with an emphasis on avoiding substitutions and managing complexity in the integration process.

Discussion Character

  • Exploratory, Problem interpretation

Approaches and Questions Raised

  • The original poster expresses difficulty in finding useful substitutions and mentions that integration by parts leads to chaotic results. Another participant suggests rewriting the integral to facilitate a substitution.

Discussion Status

Some participants indicate they have arrived at an answer, expressing a desire for quicker recognition of integration techniques. However, the discussion does not reach a consensus on the methods used or the challenges faced.

Contextual Notes

There is a mention of imposed constraints regarding the use of substitutions, which may affect the approaches considered by participants.

1MileCrash
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Find the integral of

X^3sin(x^2)

No useful substitutions I can find, integration by parts gets chaotic.
 
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Write it as x(x2)sin(x2) and begin with substitution u = x2.
 
Got the answer. Thank you.

I wish I were able to recognize these things more quickly.
 
1MileCrash said:
Got the answer. Thank you.

I wish I were able to recognize these things more quickly.
Practice, practice, practice ...
 

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